Transport elements, such as tubes, cables, hoses, wires, wire bundles and the like, are widely used in a great variety of applications. For example, a jet airliner contains approximately 3,000 custom-designed metal tubes in a number of different systems including the hydraulic system, pneumatic system, fuel system, drainage system, fire suppression system and the like. In many of these applications, the tubes must be carefully designed in order to be manufacturable and installable. For example, the design of each tube carried by a jet airliner typically takes about 40 hours on average.
A tube is one type of transport element that poses a number of challenges in its design due to limitations upon the way in which the tube may be bent as described below. By way of background, tubes are composed of straight sections joined by circular arcs. As a result of constraints placed upon tube design by the manufacturing process, the straight sections and circular arcs each have a minimum length such that it is impossible to have an arbitrarily small bend, and one bend cannot begin an arbitrarily small distance from another bend. As shown in FIG. 1, a tube generally includes a starting point, designated the A-end, and an ending point, designated the B-end, and at least one bend defined or determined by a node, e.g., N1, therebetween. With respect to the node terminology, it is noted that for certain classes of curves, nodes are also called control polygon vertices. Since the straight segments 2 of a tube are joined by arcuate segments 4, the tube does not pass through the nodes which, instead, are imaginary points where the two adjacent straight sections would intersect if extended far enough as designated by N1 and N2 in FIG. 1. A transport element may therefore be defined in terms of its nodes supplemented by some additional information depending upon the type of transport element. In the case of a metal tube, for example, the additional information may include the radius at which the tube is bent at each bend, although typically a metal tube is bent at the same radius at each bend. For other types of transport elements, such as hoses, the additional information may include the order of the spline that defines the type of curved route followed by the transport element, the tangent direction of the transport element at each node, etc..
While nodes are an effective representation of a tube, the use of nodes in the design of tubes may sometimes create problems. For example, a tube design may require a predetermined standoff S at the B-end, such as for tool access, as shown in FIG. 2. In this regard, standoff refers to the length of the straight segment adjacent to either the A-end or the B-end. Traditional design practice is to position the node N a sufficient distance from the B-end to provide the designated standoff. However, if the segment of the tube upstream of node N is modified as shown in FIG. 3, the standoff S′ will shrink to an unacceptable level even though the node that defined the standoff was supposedly correct. Even though the node does not define the standoff directly and may therefore be somewhat problematic during the design process, nodes are frequently utilized in the design of tubes because of their simplicity and convenience.
When designing the route of a transport element, such as tube, a designer initially develops a gross route or sketch which is a simple description of a relatively restricted set of possible routes. The gross route may be developed mentally by the designer and is typically based upon the starting and end points as well as various obstacles, way-points, etc. that are located therebetween. In designing the gross route, a designer generally designs it to comply with a number of extrinsic or situation-dependent constraints that include, for example, the minimum separation from structures or other tubes, requirements that the tube be parallel to certain structures, requirements that the tube penetrate certain structures within a particular zone, etc. While termed a route, the gross route that is designed generally defines a class of topologically equivalent routes that satisfy the various constraints. Based upon the gross route, a designer can select a specific route for the transport element. Unfortunately, designers do not generally select the specific route to be optimal for a transport element and have no techniques for doing so.
Given a gross route, the specific route of a transport element is generally designed by manual drafting in a computer-aided design (CAD) system such as CATIA. This manual drafting is typically a slow and difficult process. In the case of a metal tube, it may appear that a tube centerline extending from the A-end to the B-end may be easily constructed by merely specifying some intermediate way-points at which the tube will be attached to structures at particular orientations and then having the CAD system fill in straight lines and tangential circular arcs between the A-end, the B-end and the intermediate way-points. The difficulty lies, however, in ensuring that the resulting route is manufacturable, satisfies engineering constraints and is optimal.
In the case of metal tubes, for example, the manufacturing process dictates a variety of intrinsic constraints, such as minimum bend angle, maximum bend angle, minimum straight section length between bends, constraint bend radius, etc. These constraints typically arise from the nature of tube bending machines. Generally, a tube bending machine starts with a straight piece of tubing stock and repeatedly performs various operations including shooting out a certain length of tube stock to generate a straight section, bending or wrapping the tube around a circular die to generate a circular arc, and rotating the tube about its longitudinal axis to establish a new plane for the next bend. Typically, it is expensive to change the circular die. As such, each bend in a tube preferably has the same radius. In addition, the machine must be able to grip the stock during the formation of a bend such that the bending head has a certain amount of clearance, i.e., a new bend cannot be started arbitrarily close to the previous bend. The requirement that the tube stock be gripped during bending operations therefore results in the requirement of a minimum straight section length. These constraints are termed intrinsic constraints since they apply to every tube no matter where the tube is situated.
In designing the route for a tube on a CAD system, the designer essentially lays down one straight segment after another or, equivalently, defines one node after another with the circular arcs connecting these straight sections being interpolated automatically. A variety of CAD systems are available including CATIA, Solid Edge and Pro/Engineer. Typically, these systems offer the designer assistance in placing the next segment by providing something like a compass, that is, a graphical icon depicting a local three-dimensional (3D) coordinate system. In CATIA and similar systems, the designer can place the compass anywhere in the scene, usually by using existing geometry as a base of reference. For example, if the designer wants the next section of a tube to be parallel to a particular facet of a solid, the designer can place the compass on the facet, and indicate which of its three planes is to be “paralleled.” The next tubing section is automatically constrained to lie parallel to that plane. The compass is therefore essentially a way of turning an inherently 2-D input device, such as a mouse, into an effective 3-D input device.
The compass is a particularly flexible tool because the designer can choose any of its planes or axes to constrain the location of the next segment. The compass can also be used to establish planes that cannot be penetrated during the drawing process. For example, when routing a tube near a piece of machinery from which there must be a certain amount clearance, the designer can use the compass to establish a plane defining an impenetrable barrier at the appropriate distance from the machinery. Therefore, any attempt to move the mouse beyond that plane will fail and the system will provide some kind of signal, e.g., a flash, a buzz, or simple refusal to draw beyond the barrier.
Nevertheless, the compass, and all the operations it supports, still amount to an essentially manual drafting process. As shown in FIGS. 4a-4d, the designer draws one segment of the tube, which is then frozen, and then proceeds to the next section, and so on. With respect to the sequential example provided by FIGS. 4a-4d, the tube design is frozen to the left of the dotted line. As soon as a new segment is drawn, the necessary circular arc is interpolated between the new segment and the previous segment as indicated by the dashed lines in FIGS. 4a-4d. Most CAD systems allow the designer to input minimum bend angles, minimum straight segment lengths and the like and, if the designer draws a tube segment that violates these rules, a warning is provided which may simply involve the failure to construct the tube as requested. However, conventional CAD systems do not provide the designer with any alternative suggestions for a comparable tube segment that would comply with the rules and does not consider any redesign of the previously frozen portion of the tube design. Following completion of a portion of the tube routing, the CAD system simply checks the route for compliance with various rules in a post hoc manner. For example, the CAD system may check the route to ensure that the segment just designed has a certain minimum length. One example of the CAD system for routing transport elements that offer a post hoc check, albeit a rapid and interactive one, is the TubeExpert CAD program provided by Oettinger Gmbh of Oberursel, Germany. If the post hoc check determines that one or more of the segments does not comply with the rules, the route of the transport element must be redesigned, thereby consuming a significant amount of additional time and resources.
Once a transport element is designed, it may be desirable to modify it. For example, consider the initial route of a tube depicted in FIG. 5. If the nodal point N4 were moved upward, a typical CAD system would change only that portion of the route of the tube that is local to the node that is being moved. In other words, typical CAD systems would change only the straight segments N3-N4 and N4-N5, as well as the arcs that connect these straight segments. The remainder of the tube would remain fixed since conventional CAD systems do not embody any concept of global optimality for transport elements. In other words, conventional CAD systems do not support global changes to the route of a transport element as a result of local influences or changes. As shown in FIG. 6, modern CAD systems therefore view a tube as a linkage of ball joints and telescoping joints. As N4 moves upwards, the joints or links that are circled in dashed lines in FIG. 6 are free to accommodate this movement, but the other joints or links are frozen so that the transformation of the route of the tube occurs as shown in FIG. 7.
The portion of the transport element that drives or originates the modification need not be a node. For example, the designer may wish to move an entire straight segment, such as the segment between N3 and N4. If this segment were moved upward such as in response to the moving of a clamp through which this segment of the tube must pass, the route of the tube would be varied as shown in FIG. 8 in which the clamp is indicated by a rectangle. It should be noted, however, that the tube still changes shape only via the minimal, local subset of joints or links necessary to allow the upward motion of the N3-N4 segment.
Conventional CAD systems permit the route of tubes to be pushed or pulled into another shape only so long as the tube continues to have the same number of nodes. Thus, conventional CAD systems do not permit one route of a tube to be continuously deformed into another route unless those routes have the exact same number of nodes or bends. Stated another way in CAD terminology, a tube cannot be “rubber banded” into another tube unless they both have the same number of bends. Accordingly, if the route of the tube must have a different number of nodes, the existing route cannot simply be pushed or pulled into another shape, but a new set of nodes must be determined. In this regard, FIG. 9 depicts the tube extending from a fixed fitting 10 to a bulkhead 12 of an aircraft. If the position of the bulkhead changed as shown in FIG. 10, the set of nodes for the tube would also have to change. Although similar to the route depicted in FIG. 9, the route of the tube depicted in FIG. 10 would be considered a new design by conventional CAD systems and would have to be completely redesigned, i.e., conventional CAD systems do not regard the number and placement of nodes as parameters that the system is free to adjust; rather, they are seen as constants determined by the designer with which the system must work. As such, conventional CAD systems require the designer to foresee the possible future rotation of the bulkhead and to design corresponding freedom in the linkage sense of FIG. 6. Since designers cannot predict the future, this requirement may go unmet in many instances.
By way of another example, a tube may be required to be attached to a structural element 14 as shown in FIG. 11. Most modern parametric CAD systems allow the designer to represent the clamp by associating a mathematical constraint between a point, edge or face of the structural element and an intermediate segment of the tube. Thus, if the structural element were moved downward, the route of the tube may be changed on a local basis as described above and as depicted in FIG. 12. In this regard, some CAD systems also require the designer to specify the joints and links that are free to move. For example, with respect to the route of the tube depicted in FIG. 12, in order to accommodate the downward movement of the structural element, the straight segments 16 of the tube on either side of the structural element may be elongated and the intermediate tube segment 18 may be shrunk, or the intermediate tube segment may maintain a constant length while permitting the straight tube segments on either side to stretch and all four nearby angles 20 to vary. In other words, the CAD system may not necessarily have a predefined rule or principle for determining the joints and links that are free and the joints and links that are frozen and may, instead, require input from the designer.
In contrast to the downward movement of the structural element, upward movement of the structural element can cause the route of the tube to approach an illegal configuration in which the minimum bend angle would be violated at bends 22 as shown in FIG. 13. In this regard, it is important to note that angles α are conventionally measured supplementarily as indicated in FIG. 13. While the upward movement of the structural element may be accommodated either by moving the outboard clamps downward such that the tube may assume a straight line or introducing additional nodes or bends, each of these solutions requires that the tube be redesigned in the eyes of conventional CAD systems by requiring a different number and general placement of the nodes.
Therefore, while a number of CAD systems are currently available for assisting in the design of a route of a transport element, such as a tube, these CAD systems do not support as much flexibility in the design process as would be desired. In this regard, conventional CAD systems may alert the designer if a new segment does not meet a particular constraint, or if the design as a whole does not meet one or more constraints. However, conventional CAD systems do not use the constraints to drive or generate the design and/or to provide a measure of the merit of the design. In addition, modern CAD systems only support limited modification of existing routes since modern CAD systems generally only permit the sections local to the portion of the route being modified to move. As such, designers may be unable to modify an existing route of a transport element to accommodate a change in some instances and would, instead, have to redesign the set of nodes, thereby consuming additional time and resources.